detailed information: The input equation set is:
| | | | | | | | | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
| Question solving process:
Add both sides of equation (1) to both sides of equation (2) ,the equations are reduced to:
| | | | | | | | | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Multiply both sides of equation (1) by 10 Divide the two sides of equation (1) by 3, the equation can be obtained: , then add the two sides of equation (9) to both sides of equation (8), the equations are reduced to:
| | | | | | | | | | | B | + | | C | + | | D | + | | | 8 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
| | | | | | | | | | | B | + | | C | + | | D | + | | | 8 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | | | | | | | | B | + | | C | + | | D | + | | | 8 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Subtract both sides of equation (2) from both sides of equation (8) ,the equations are reduced to:
| | | | | | | | | | | C | + | | D | + | | | 5 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | - | 1 2 | C | | - | 1 4 | E | + | | | 1 4 | F | = | | 0 | (12) | , then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| | | | C | + | | D | + | | | 5 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (3) by 2, the equation can be obtained: | - | 1 2 | C | | - | 1 4 | E | + | | | 1 4 | F | = | | 0 | (13) | , then add the two sides of equation (13) to both sides of equation (6), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| - | 1 4 | E | | - | 3 4 | F | + | | | 1 2 | G | = | | 0 | | (6) |
| | | C | + | | D | + | | | 5 3 | E | + | | F | + | | G | + | | H | = | | 1 | | (8) |
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Add both sides of equation (3) to both sides of equation (8) ,the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| - | 1 4 | E | | - | 3 4 | F | + | | | 1 2 | G | = | | 0 | | (6) |
| | | D | + | | | 7 6 | E | + | | | 3 2 | F | + | | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (4) by 2, the equation can be obtained: | - | 1 2 | D | | - | 1 4 | E | + | | | 1 4 | F | = | | 0 | (14) | , then add the two sides of equation (14) to both sides of equation (7), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| - | 1 4 | E | | - | 3 4 | F | + | | | 1 2 | G | = | | 0 | | (6) |
| - | 1 4 | E | + | | | 1 4 | F | | -1 | G | + | | | 1 2 | H | = | | 0 | | (7) |
| | D | + | | | 7 6 | E | + | | | 3 2 | F | + | | G | + | | H | = | | 1 | | (8) |
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Add both sides of equation (4) to both sides of equation (8) ,the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| - | 1 4 | E | | - | 3 4 | F | + | | | 1 2 | G | = | | 0 | | (6) |
| - | 1 4 | E | + | | | 1 4 | F | | -1 | G | + | | | 1 2 | H | = | | 0 | | (7) |
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Divide the two sides of equation (5) by 5, the equation can be obtained: | - | 1 4 | E | + | | | 1 20 | F | + | | | 1 10 | G | = | | 0 | (15) | , then subtract both sides of equation (15) from both sides of equation (6), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| | - | 1 4 | E | + | | | 1 4 | F | | -1 | G | + | | | 1 2 | H | = | | 0 | | (7) |
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Divide the two sides of equation (5) by 5, the equation can be obtained: | - | 1 4 | E | + | | | 1 20 | F | + | | | 1 10 | G | = | | 0 | (16) | , then subtract both sides of equation (16) from both sides of equation (7), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| | | | 1 5 | F | | - | 11 10 | G | + | | | 1 2 | H | = | | 0 | | (7) |
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Multiply both sides of equation (5) by 8 Divide the two sides of equation (5) by 15, the equation can be obtained: | - | 2 3 | E | + | | | 2 15 | F | + | | | 4 15 | G | = | | 0 | (17) | , then add the two sides of equation (17) to both sides of equation (8), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| | | | 1 5 | F | | - | 11 10 | G | + | | | 1 2 | H | = | | 0 | | (7) |
| | | 32 15 | F | + | | | 19 15 | G | + | | H | = | | 1 | | (8) |
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Divide the two sides of equation (6) by 4, the equation can be obtained: , then add the two sides of equation (18) to both sides of equation (7), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
| | | | | 32 15 | F | + | | | 19 15 | G | + | | H | = | | 1 | | (8) |
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Multiply both sides of equation (6) by 8 Divide the two sides of equation (6) by 3, the equation can be obtained: , then add the two sides of equation (19) to both sides of equation (8), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
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Multiply both sides of equation (7) by 7 Divide the two sides of equation (7) by 3, the equation can be obtained: , then add the two sides of equation (20) to both sides of equation (8), the equations are reduced to:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
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Multiply both sides of equation (8) by 3 Divide both sides of equation (8) by 13, get the equation:, then subtract both sides of equation (21) from both sides of equation (7), get the equation:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
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Multiply both sides of equation (7) by 2 Divide both sides of equation (7) by 5, get the equation:, then add the two sides of equation (22) to both sides of equation (6), get the equation:
| | | | | | | - | 5 4 | E | + | | | 1 4 | F | + | | | 1 2 | G | = | | 0 | | (5) |
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Divide both sides of equation (7) by 2, get the equation:, then add the two sides of equation (23) to both sides of equation (5), get the equation:
Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 16, get the equation:, then add the two sides of equation (24) to both sides of equation (5), get the equation:
Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 8, get the equation:, then add the two sides of equation (25) to both sides of equation (4), get the equation:
Multiply both sides of equation (6) by 5 Divide both sides of equation (6) by 8, get the equation:, then add the two sides of equation (26) to both sides of equation (3), get the equation:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 5, get the equation:, then subtract both sides of equation (27) from both sides of equation (4), get the equation:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 5, get the equation:, then subtract both sides of equation (28) from both sides of equation (3), get the equation:
Multiply both sides of equation (5) by 4 Divide both sides of equation (5) by 5, get the equation:, then add the two sides of equation (29) to both sides of equation (2), get the equation:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 5, get the equation:, then add the two sides of equation (30) to both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |